Control device and method for establishing the rotor angle of a synchronous machine

ABSTRACT

A method and a device for establishing the rotor angle of a synchronous machine. In one embodiment, the method includes the steps of feeding at least one initial voltage pulse of predefinable pulse length and pulse height into the stator of the synchronous machine, detecting the respective current response to the at least one initial voltage pulse, determining the respective phase difference on the basis of the respective detected current response, establishing at least one first estimated value by comparing the current response with a current response characteristic curve of the synchronous machine, establishing at least one second estimated value by comparing the phase difference with a phase difference characteristic curve of the synchronous machine, forming a multiplicity of differences between each of the first estimated values and each of the second estimated values, and determining an initial estimated value for the rotor angle of the synchronous machine on the basis of the determined difference having the lowest value.

BACKGROUND OF THE INVENTION

The invention relates to a control device and a method for establishingthe rotor angle of a synchronous machine, in particular at standstill ofa synchronous machine of an electric drive system of an electricallyoperated vehicle.

It is becoming apparent that, in the future, electronic systems thatcombine new energy storage technologies with electric drive technologywill be used increasingly both in stationary applications, such as inwind turbines or solar installations, and in vehicles, such as hybrid orelectric vehicles.

When regulating a synchronous machine, for example in an electric drivesystem of an electrically operated vehicle, the knowledge of theposition of the rotor relative to the stator of the synchronous machineplays a central role. In order to provide a required torque with asynchronous machine, a rotating electric field is generated in thestator of the machine and rotates synchronously with the rotor. For thegeneration of this field, the current angle of the rotor is required forthe regulation process.

One possibility for determining the rotor angle lies in theimplementation of a sensor in the synchronous machine, said sensor beingable to detect the rotor angle. Exemplary sensor types includeincremental sensors, resolvers, Vogt sensors and digital Hall sensors.

A further possibility for determining the rotor angle lies in sensorlessdetermination methods. For example, different methods for sensorlessdetermination of a rotor angle of a synchronous machine are known fromthe documents by Schroedl, M.: “Sensorless control of AC machines at lowspeed and standstill based on the INFORM method”, Industry ApplicationsConference, 1996, 31^(st) IAS Annual Meeting; Ostlund, M., Brokemper,M.: “Initial rotor position detections for an integrated PM synchronousmotor drive”, Industry Applications Conference, 1995, 30^(th) IAS AnnualMeeting; Linke, M., Kennel, R., Holtz, J.: “Sensorless speed andposition control of synchronous machines using alternating carrierinjection”, Electric Machines and Drives Conference, 2003, IEMDC'03; andBraun, M., Lehmann, O., Roth-Stielow, J.: “Sensorless rotor positionestimation at standstill of high speed PMSM drive with LC inverteroutput filter”, 2010 IEEE International Conference on IndustrialTechnology (ICIT).

Documents DE 10 2008 042 360 A1 and WO/2009/047217 A2 each disclose amethod for determining the rotor angle of a synchronous machine atstandstill with the aid of iterative test pulses.

SUMMARY OF THE INVENTION

The present invention, in accordance with one aspect, creates a methodfor establishing the rotor angle of a synchronous machine, said methodcomprising the steps of feeding at least one initial voltage pulse ofpredefinable pulse length and pulse height into the stator of thesynchronous machine, detecting the respective current response to the atleast one initial voltage pulse, determining the respective phasedifference on the basis of the respective detected current response,establishing at least one first estimated value by comparing the currentresponse with a current response characteristic curve of the synchronousmachine, establishing at least one second estimated value by comparingthe phase difference with a phase difference characteristic curve of thesynchronous machine, forming a multiplicity of differences between eachof the first estimated values and each of the second estimated values,and determining an initial estimated value for the rotor angle of thesynchronous machine on the basis of the determined difference having thelowest value.

The present invention, in accordance with a further aspect, creates acontrol device for establishing the rotor angle of a synchronousmachine, wherein the control device is designed to carry out a method inaccordance with an aspect of the invention.

In accordance with a further aspect, the present invention creates anelectric drive system having a control device according to the inventionand a synchronous machine, wherein the control device is designed tocontrol the synchronous machine in accordance with the established rotorangle.

One concept of the present invention is to implement a sensorless rotorangle determination for synchronous machines, in particular atstandstill. Here, the determination method is based on the generation oftest voltage pulses in predefinable sequence, these test voltage pulsesbeing fed into the stator inductors of the synchronous machine. Therotor angle can then be determined based on the measured currentresponses. Here, the determination is carried out both for salient-polemachines and for non-salient-pole machines. Depending on the necessaryor desired accuracy of the rotor angle determination, the procedure canbe divided into two test portions, wherein, in the first portion, one ortwo voltage pulses is/are generated, such that, when comparing thecurrent response and the phase difference of the phase current from thephase of the voltage, a rough estimation can be established for thed-axis. This rough estimation can then be used in a second portion inorder to feed pairs of voltage pulses, which are grouped symmetricallyabout the estimated d-axis, into the synchronous machine and to specifythe rough estimated value for the d-axis via an adjustment computationalgorithm, for example a linear regression of the current responses orphase differences.

A significant advantage of this approach is that the number of necessaryvoltage pulses can be minimized depending on the necessary or desiredaccuracy. Alternatively, with constant pulse number, the accuracy of theangle determination can be increased compared to known methods. Inaddition, the robustness and reliability of the rotor angledetermination is considerably better compared to known sensorlessmethods. This enables the use of the rotor angle determination forexample in production vehicles with electric drive system.

In addition, the extent to which the rotor angle determination isdependent on the accuracy or quality of the current sensors used isreduced. More favorable current sensors can therefore be used, whichlowers the manufacturing costs of the electric drive system. The rotorangle determination can also be carried out in a self-diagnosisoperating mode without the need for external calibration.

Furthermore, there is the advantage that there is no build-up ofsignificant torque over the course of the determination procedure, andtherefore the position of the rotor of the synchronous machine is notchanged, or is not significantly changed, by the applied voltage pulses.The development of noise and waste heat caused by the applied voltagepulses is thus reduced.

The risk of undesired torque formation at standstill of the synchronousmachine is advantageously reduced, particularly in the case ofsalient-pole machines, since the saturation pulses can only be appliedin the direction of the estimated d-axis.

In accordance with an embodiment of the method according to theinvention, the method may also comprise the step of feeding amultiplicity of calibration voltage pulses of predefinable pulse lengthand pulse height into the stator of the synchronous machine, detectingthe angle-dependent calibration current responses to the calibrationvoltage pulses, determining the angle-dependent calibration phasedifferences on the basis of the respective detected calibration currentresponse, and determining the current response characteristic curve andthe phase difference characteristic curve of the synchronous machine onthe basis of the angle-dependent calibration current responses andcalibration phase differences respectively. Characteristic curves canthus be readjusted continually during the operation of the electricdrive system.

In accordance with a further embodiment of the method according to theinvention, calibration voltage pulses can be fed into the stator of thesynchronous machine in pairs offset in each case by 180° with respect tothe stator angle. The risk of introducing undesired torques into thesynchronous machine is thus reduced.

In accordance with a further embodiment of the method according to theinvention, the determination of the initial estimated value for therotor angle of the synchronous machine may comprise the formation of themean value of the first and second estimated values involved in thesmallest difference.

In accordance with a further embodiment of the method according to theinvention, the synchronous machine may comprise a non-salient-polemachine, wherein at least two initial voltage pulses, which bring thenon-salient-pole machine into saturation, are fed into the stator of thenon-salient-pole machine.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of embodiments of the invention willemerge from the following description with reference to the accompanyingdrawings.

In the drawings:

FIG. 1 shows a schematic illustration of an electric drive system with asynchronous machine according to an embodiment of the present invention;

FIG. 2 shows a schematic illustration of voltage pulses and currentresponses thereof in a synchronous machine according to a furtherembodiment of the present invention;

FIG. 3 shows a schematic current/time graph for the current response ofa synchronous machine according to a further embodiment of the presentinvention;

FIG. 4 shows a schematic phase difference graph for the phase differencebetween current and voltage of a synchronous machine according to afurther embodiment of the present invention;

FIG. 5 shows a schematic current/time graph for the current response ofa non-salient-pole machine according to a further embodiment of thepresent invention;

FIG. 6 shows a schematic phase difference graph for the phase differencebetween current and voltage of a non-salient-pole machine according to afurther embodiment of the present invention;

FIG. 7 shows a schematic current/time graph for the current response ofa salient-pole machine according to a further embodiment of the presentinvention;

FIG. 8 shows a schematic phase difference graph for the phase differencebetween current and voltage of a salient-pole machine according to afurther embodiment of the present invention;

FIG. 9 shows a schematic current/time graph for the estimation of thed-axis of a rotor of a synchronous machine according to a furtherembodiment of the present invention;

FIG. 10 shows a schematic phase difference graph for the estimation ofthe d-axis of a rotor of a synchronous machine according to a furtherembodiment of the present invention;

FIG. 11 shows a schematic current/time graph for more accuratedetermination of the d-axis of a rotor of a synchronous machineaccording to a further embodiment of the present invention;

FIG. 12 shows a schematic phase difference graph for more accuratedetermination of the d-axis of a rotor of a synchronous machineaccording to a further embodiment of the present invention;

FIG. 13 shows a schematic illustration of a method for estimating therotor angle of a synchronous machine according to a further embodimentof the present invention; and

FIG. 14 shows a schematic illustration of a further method fordetermining the rotor angle of a synchronous machine according to afurther embodiment of the present invention.

DETAILED DESCRIPTION

Like reference signs generally denote similar or functionally likecomponents. The schematic signal and parameter curves shown in thefigures are merely exemplary and are illustrated in an idealized mannerfor reasons of clarity. It goes without saying that deviating signal andparameter curves can be produced in practice due to deviating boundaryconditions, and that the illustrated signal and parameter curves servemerely to illustrate principles and functional aspects of the presentinvention.

Within the meaning of the present invention, synchronous machines areelectric machines in which a constantly magnetized rotating part orrotor is driven synchronously by a time-dependent magnetic rotatingfield in the surrounding non-rotating part or stator by magneticinteraction, such that the rotor performs a movement synchronous to thevoltage conditions in the stator, that is to say the rotational speedover the number of pairs of poles is dependent on the frequency of thestator voltage. Synchronous machines within the meaning of the presentinvention may be three-phase synchronous machines for example, which forexample are formed as revolving-armature or stationary-armature machinesthat have a rotor and a stator. Furthermore, synchronous machines withinthe meaning of the present invention may comprise salient-pole machinesor non-salient-pole machines. Non-salient-pole machines have anaxis-independent inductance of the rotor, whereas salient-pole machineshave a distinguished pole axis, also referred to as a d-axis, in thedirection of which the magnetizing inductance is greater than in thedirection of the pole gaps, also referred to as the q-axis, due to thesmaller air gap. The methods and control devices mentioned hereinaftercan, in principle, be used equally for non-salient-pole machines andsalient-pole machines unless reference is made hereinafter explicitly todifferent handling of synchronous machine types.

FIG. 1 shows a schematic illustration of an electric drive system 100with a synchronous machine 101, into which three-phase current can befed. Here, a d.c. voltage provided by a d. c. link 103 is converted intoa three-phase a.c. voltage via an inverter in the form of apulse-width-modulation inverter 102. The d.c. link 103 is fed by astring 104 formed of battery modules 105 connected in series. In orderto meet the requirements of power and energy defined for a respectiveapplication, a plurality of battery modules 105 are often connected inseries in a traction battery 104.

The electric machine 101 may, for example, be a synchronous machine 101which has stator inductors L. By way of example, the synchronous machine101 is a three-phase synchronous machine. It is also possible inprinciple however to provide a different number of phases for thesynchronous machine. Here, the regulation of the synchronous machine 101in the electric drive system plays a central role. In order to provide arequired torque with a synchronous machine, a rotating electric field isgenerated in the stator of the machine and rotates synchronously withthe rotor. For the generation of this field, the current angle of therotor is required for the regulation process.

The electric drive system 100 therefore comprises a control device 10,which is coupled to the synchronous machine 101 and is designed tocontrol the synchronous machine 101 or to regulate the operationthereof. For this control or regulation, the control device 10 utilizesthe time-dependent rotor angle of the rotor of the synchronous machine101 with respect to the stator of the synchronous machine 101. Here, thecontrol device 10 may detect electric operating parameters at the inputconnections of the synchronous machine 101 via an interface 106. Forexample, the control device 10 may be designed to establish themomentary phase currents and/or the momentary phase voltages at theinputs of the synchronous machine 101 via the interface 106. Currentsensors such as shunt resistors, magnetoresistive resistors, sensorpower semiconductors or Hall sensors, or voltage sensors can be used todetect the phase currents and phase voltages.

The way in which the control device 10 establishes the rotor angle of asynchronous machine 101, in particular at standstill of the synchronousmachine 101, will be explained with reference to FIGS. 2 to 12 as wellas the correlations that are to be taken into consideration during thisprocess. Here, the control device 10 may in particular implement one orboth of the methods 20 and 30 explained with reference to FIGS. 13 and14 respectively.

FIG. 2 shows a schematic illustration of non-saturating voltage pulses Uand the current responses I thereof in a salient-pole machine over time.The direct-axis components of current I_(d) and quadrature-axiscomponents of current I_(q) of a permanently excited synchronous machinebehave in a manner dependent on the rotor inductance L_(d) in polar axisdirection and on the rotor inductance L_(q) in pole gap direction and onthe applied voltage U_(d) or U_(q) respectively as follows:

dI _(d) /dt=L _(d) ⁻¹ ·U _(d)

dI _(q) /dt=L _(q) ⁻¹ ·U _(q).

This is true for the standstill of the rotor of the synchronous machineand with constant rotor flux over time if it can also be assumed thatthe reactance of the rotor is only insignificantly dependent on theohmic resistance. In addition, it is assumed that the pole shoe(s)is/are not operated in saturation, that is to say that the relationshipbetween current and magnetic flux is linear and the respectiveinductance is not dependent on the current intensity.

With a voltage pulse of predefined length and predefined constantintensity, the current therefore rises linearly with the length of thevoltage pulse up to a maximum value I_(max). This maximum value I_(max)is dependent here on the respective inductance L_(d) or L_(q).

FIG. 3 shows the dependence of the maximum current value I_(max), thatis to say the current response I to a voltage pulse, along the rotorangle β. The rotor angle β is the angle enclosed by the q-axis and theprimary stator axis. In FIGS. 3 to 10, which each show parameter curvesin accordance with the rotor angle β, the rotor angle β is illustratedhere over a full rotor revolution in each case, that is to say 360°. Thesetting of the reference angle of 0° in the negative q-axis direction ismerely exemplary in this case. It is therefore conceivable to also setthe rotor angle β to other reference angles. For improved orientation,the angle 90° is given as the d-axis direction or polar axis direction,and the angle 180° is given as the q-axis direction or pole gapdirection in each of FIGS. 3 to 10.

FIG. 4 shows the dependence of the phase difference Δ between thevoltage pulse U and the current response I along the rotor angle β for asalient-pole machine. The current angle β_(I) is defined here as

β₁=tan⁻¹(I _(q)/I_(d)).

The voltage angle β_(U) is accordingly defined as

β_(U)=tan⁻¹(U _(q) /U _(d)).

In the case of a non-salient-pole machine, a behavior is given both forthe current response I and for the phase difference Δ, said behaviordemonstrating rotor-angle-dependent behavior only in saturation. Abehavior of this type is shown by way of example in FIGS. 5 and 6 forthe current response I and the phase difference Δ of a non-salient-polemachine. At high currents, the pole shoe of the non-salient-pole machineis saturated and the relationship between current and magnetic flux hasnon-linearities, that is to say the inductance depends on the currentintensity and on the rotor angle. In a first approximation (withdependence purely on rotor angle and current intensity), the currentresponse curve I illustrated in FIG. 5 is produced for thenon-salient-pole machine in accordance with the rotor angle β. FIG. 6shows the corresponding dependence of the phase difference Δ on therotor angle β.

By contrast, in the case of a salient-pole machine, the angulardependence without saturation caused by the different polar axis andpole gap inductances L_(d) and L_(q) respectively is superimposed by theangular dependence with saturation. The curve illustrated in FIG. 7 forthe current response curve I and the curve illustrated in FIG. 8 for thephase difference Δ are thus produced for the salient-pole machine inaccordance with the rotor angle β.

In order to determine or estimate the rotor angle β of the rotor, one ormore test voltage pulses of specific length and direction, that is tosay angular dependence with respect to the stator coordinate system,is/are fed into the synchronous machine in various method portions andthe respective current responses are established. The current responsecan be produced for example by measuring the maximum current I_(max) orby integrating the current intensity over the length of the test voltagepulse. Once the current response has been determined, the synchronousmachine can be switched into freewheeling operation via a correspondingcontrol of the pulse-width-modulation inverter for a predefinable periodof time between the voltage pulses in order to reduce more quickly thecurrent impressed into the synchronous machine.

The phase difference for the respective test voltage pulse can then beestablished from the detected current response and the voltage pulses.The rotor angle β is then estimated by means of the two measured valuesfor the current response I and the phase difference Δ with the aid ofthe characteristic curves illustrated in FIGS. 5 to 8 in accordance withthe type of synchronous machine. Reference is made here by way ofexample in each of FIGS. 9 to 12 to a salient-pole machine, wherein themethod for determining the rotor angle β in principle functionssimilarly for a non-salient-pole machine with adaptation of theappropriate characteristic curves.

Firstly, the characteristic curves can be calibrated at the start of therotor angle determination. For example, by means of simulation withspecial models, it is possible to test, even before manufacture of thefirst prototype of a machine, whether the corresponding synchronousmachine is suitable in principle for the rotor angle determinationmethods presented here. If this is the case, a calibration procedure canbe carried out once or repeatedly, for example with each start of theelectric drive system, in order to establish the characteristic curvesof the respective synchronous machine for the current response I and thephase difference Δ.

To this end, a plurality of pairs of in each case two test voltagepulses of fixed amplitude can be applied to the synchronous machine, andthe respective current response established. The pairs of test voltagepulses should each be applied offset by 180° in relation to one anotherin order to avoid an introduction of an undesired torque into themachine. In addition, the decay of the current in the synchronousmachine can be accelerated by the offset by 180°. The number of pairs oftest voltage pulses should be selected such that they are distributeduniformly over one electric revolution. When establishing the currentresponse, the respective target voltage and the respective d.c. linkvoltage are stored. The detected current is then dependent on the storedvoltages, the inductances L_(d) and L_(q) of the synchronous machine,and the current rotor angle to be determined.

If the inductances or the voltages are sufficiently well known oridentifiable, a parameter identification of the corresponding voltagesor inductances can additionally be carried out via the known properties.

The characteristic curves established via the first calibration are thenused to form the basis of the initial angle determination steps shown inFIGS. 9 and 10.

With reference to FIGS. 9 and 10, an initial voltage pulse can beapplied to the synchronous machine in a first step in order to obtain afirst estimation for the rotor angle β from the characteristic curvesfor the current response I and the phase difference Δ. To this end, inthe case of salient-pole machines, a non-saturating initial voltagepulse can be selected so as not to generate any torque in thesynchronous machine. By contrast, in the case of non-salient-polemachines, it is necessary to use saturation pulses in order to drive themachine in saturation, since otherwise no rotor-angle-dependent behaviorof the synchronous machine can be provoked.

As is clear from FIG. 9, the initial voltage pulse leads to a measuredcurrent response Im. By comparison with the characteristic curve for thecurrent response I, two first estimated values for the rotor angle β,specifically β1 and β2, are produced in the angular range between 0° and180°. In the example illustrated in FIG. 9, these are approximately 30°and approximately 150°. As is clear from FIG. 10, the comparison of theestablished phase difference Am with the characteristic curve for thephase difference Δ likewise leads to two second estimated values for therotor angle β, specifically β3 and β4. In the present example, these areapproximately 20° and approximately 60°.

Differences between each of the first estimated values and each of thesecond estimated values can then be formed for the rotor angle β—in thepresent example this corresponds to four differences (β1−β3, β4−β1,β3−β2 and β2−β4). In the case of the smallest difference, it can then beassumed that the respective first and second estimated values are themost accurate estimated values. An initial estimated value can thereforebe formed as a mean value of the two most accurate estimated values.

For the salient-pole machine, the resolution of the rotor angle is onlycarried out between 0° and 180°, since the inductance change withnon-saturating voltage pulses is produced from the viewpoint of thestator with double electric frequency. By contrast, in the case of anon-salient-pole machine, two initial voltage pulses are necessary inorder to determine the initial estimated value for the rotor angle,since with saturation pulses there is a periodic behavior over 360° forthe current response and the phase difference.

Once the initial voltage pulse or the initial voltage pulses has/havebeen applied, the initial estimated value can then be refined. This maythen be desirable for example if an accurate rotor angle determinationthat is more robust than the initial estimation is necessary. Thestarting point for refining the initial estimated value is thedetermination of a first estimated value dl for the d-axis on the basisof the initial estimated value.

As illustrated by way of example in FIGS. 11 and 12, one or more pairsof refinement voltage pulses can be applied to the synchronous machineand are each distributed symmetrically and the first estimated value d1for the d-axis. For example, the angular distance x from the firstestimated value d1 for the d-axis can be identical in each case for arefinement voltage pulse pair. By way of example, two refinement voltagepulse pairs are shown in each of FIGS. 11 and 12, wherein generally 2n,n>1, pulse pairs are also possible however.

For the response current, refinement current value pairs M1 and M2 andalso M3 and M4 are given here. Similarly, refinement phase differencepairs N1 and N2 and also N3 and N4 are given for the phase difference.With the refinement on the basis of the characteristic curve for thecurrent response I, linear regressions are formed on both sides of theestimated d-axis by the refinement voltage values M1 and M3 and M2 andM4 arranged on this side respectively. Two regressions lines K1 and K2,of which the abscissa value of the point of intersection gives a refinedestimated value d2 for the d-axis, are thus produced. Similarly, aregression curve of which the abscissa value at an ordinate value ofzero gives a further refined estimated value d3 for the d-axis can beproduced by all refinement phase differences N1 to N4. Again, arefinement estimated value for the d-axis can be established on thebasis, for example, of the estimated values d2 and d3 refined by thecurrent response evaluation and the phase difference evaluation, forexample by forming a mean value. A corresponding refinement estimatedvalue for the rotor angle β can therefore be deduced.

Alternatively or additionally to the procedure described in FIGS. 11 to12, a renewed comparison with the characteristic curves for the currentresponse I and the phase difference Δ can be performed for therefinement current value pairs and refinement phase difference pairs.With amended d.c. link voltage, a new calibration or readjustment of thevoltage pulse pairs may also be carried out in some circumstances. Inaddition, it may be possible, instead of forming linear regressioncurves from the established refinement current values M1 to M4 and fromthe established refinement phase differences N1 to N4, to establishestimated curves for the current response value and the phase differenceby means of an adjustment computation, for example by means of anestimation via the method of the smallest square.

Furthermore, a curve adaptation of the current response curve and of thephase difference curve can be performed with all detected measuredvalues, and the argument can be equated with both adapted curves with90° or 180° in order to establish a refinement estimated value for thed-axis.

In the case of salient-pole machines, two saturating voltage pulses canadditionally be fed in opposite directions along the established d-axisdirection once the rotor angle estimated value has been refined so as toresolve the 180° inaccuracy. For non-salient-pole machines, this is nolonger necessary, since two saturation pulses have already been fed inthe initial step for exact determination of the position of the rotor.

Once all determination steps have been completed, the voltage intensityof the test voltage pulses can be readjusted for subsequent methodrepetitions by comparing a target current value of the current responseswith the characteristic curves. Here, a factor F can be established forthe d.c. link voltage, with which the characteristic curves can becalibrated in order to eliminate the dependence on the fluctuating d.c.link voltage.

FIG. 13 shows a schematic illustration of a method 20 for establishingthe rotor angle of a synchronous machine, in particular a synchronousmachine 101 as illustrated by way of example in FIG. 1. Here, the method20 can utilize the correlations explained in conjunction with FIGS. 2 to12. In a first step 21, at least one initial voltage pulse ofpredefinable pulse length and pulse height is fed into the stator of thesynchronous machine. In a second step 22, the respective currentresponse Im to the at least one initial voltage pulse is detected. Then,in step 23, the respective phase difference Am is determined on thebasis of the respective detected current response Im.

In steps 24 and 25, at least one first estimated value β1 and β2respectively can be established by comparing the current response valueIm with a current response characteristic curve I of the synchronousmachine on the one hand, and at least one second estimated value β3 andβ4 respectively can be estimated by comparing the phase difference Δmwith a phase difference characteristic curve Δ of the synchronousmachine on the other hand. In a step 26, a multiplicity of differencesbetween each of the first estimated values β1, β2 and each of the secondestimated values β3, β4 can be formed on the basis of the estimatedvalues, such that, in a step 27, an initial estimated value for therotor angle β of the synchronous machine can be determined on the basisof the determined difference having the lowest value.

Should a more accurate estimation of the rotor angle β be necessary, afirst estimated value d1 for the d-axis of the synchronous machine canbe determined on the basis of the initial estimated value for the rotorangle β. Here, at least one refinement voltage pulse pair ofpredefinable pulse length and pulse height is fed into the stator of thesynchronous machine, wherein the refinement voltage pulse pairs aredistanced from the first estimated value d1 for the d-axis of thesynchronous machine by the same angular value −x or +x in differentdirections. The (rotor-)angle-dependent refinement current responses tothe refinement voltage pulses can then be detected, on the basis ofwhich the angle-dependent refinement phase differences can then bedetermined.

For the angle-dependent refinement current responses, first linearregression curves K1 and K2 can be produced on the basis of at leastsome of the angle-dependent refinement current responses. Similarly,second linear regression curves K3 can be determined on the basis of atleast some of the angle-dependent refinement phase differences. Thesefirst and/or second linear regression curves can then be used todetermine a refined estimated value d2 for the d-axis of the synchronousmachine.

FIG. 14 shows a schematic illustration of a method 30 for establishingthe rotor angle of a synchronous machine, in particular a synchronousmachine 101 as illustrated by way of example in FIG. 1. Here, the method30 can utilize the correlations explained in conjunction with FIGS. 2 to12. In a first step 31, a first estimated value d1 is determined for thed-axis of the synchronous machine. In a second step 32, at least onerefinement voltage pulse pair of predefinable pulse length and pulseheight is fed into the stator of the synchronous machine, wherein therefinement voltage pulse pairs are distanced from the first estimatedvalue dl for the d-axis of the synchronous machine by the same angularvalue −x or +x in different directions. In a third step 33, theangle-dependent refinement current responses to the refinement voltagepulses are detected.

In a step 34, the (rotor-)angle-dependent refinement phase differencescan then be established on the basis of the respective detectedrefinement current response. These are then used as a basis for steps 35and 36, in which first estimated or linear regression curves aredetermined on the basis of at least some of the angle-dependentrefinement current responses and second estimated or linear regressioncurves are determined on the basis of at least some of theangle-dependent refinement phase differences. Lastly, in step 37, arefined estimated value d2 for the d-axis of the synchronous machine canbe determined on the basis of the first and/or second estimated orlinear regression curves.

Here, the estimated curves can be established by an adjustmentcomputation, for example via an estimation in accordance with the methodof the smallest square. By way of example, approximations of the firstorder, that is to say linear compensating curves, can be used here, asdescribed in conjunction with FIGS. 11 and 12.

The methods 20 and 30 in FIGS. 13 and 14 can be combined suitably suchthat, after an initial rough estimation of the rotor angle, refinementwith the aid of refinement voltage pulses is possible.

1. A method for establishing the rotor angle of a synchronous machine,said method comprising: feeding at least one initial voltage pulse ofpredefinable pulse length and pulse height into the stator of thesynchronous machine; detecting the respective current response to the atleast one initial voltage pulse; determining the respective phasedifference on the basis of the respective detected current response;establishing at least one first estimated value by comparing the currentresponse with a current response characteristic curve of the synchronousmachine; establishing at least one second estimated value by comparingthe phase difference with a phase difference characteristic curve of thesynchronous machine; forming a multiplicity of differences between eachof the first estimated values and each of the second estimated values;and determining an initial estimated value for the rotor angle of thesynchronous machine on the basis of the determined difference having thelowest value.
 2. The method according to claim 1, further comprising:determining a first estimated value for the d-axis of the synchronousmachine on the basis of the initial estimated value for the rotor angle;feeding at least one refinement voltage pulse pair of predefinable pulselength and pulse height into the stator of the synchronous machine,wherein the refinement voltage pulse pairs are distanced from the firstestimated value for the d-axis of the synchronous machine by the sameangular value in different directions; detecting the angle-dependentrefinement current responses to the refinement voltage pulses;determining the angle-dependent refinement phase differences on thebasis of the respective detected refinement current response;determining first estimated curves on the basis of at least some of theangle-dependent refinement current responses; determining secondestimated curves on the basis of at least some of the angle-dependentrefinement phase differences; and determining a refined estimated valuefor the d-axis of the synchronous machine on the basis of the firstand/or second estimated curves.
 3. The method (20) according to claim 1,further comprising: feeding a multiplicity of calibration voltage pulsesof predefinable pulse length and pulse height into the stator of thesynchronous machine; detecting the angle-dependent calibration currentresponses to the calibration voltage pulses; determining theangle-dependent calibration phase differences on the basis of therespective detected calibration current response; and determining thecurrent response characteristic curve and the phase differencecharacteristic curve of the synchronous machine on the basis of theangle-dependent calibration current responses and calibration phasedifferences respectively.
 4. The method according to claim 3, whereinthe calibration voltage pulses are fed into the stator of thesynchronous machine in pairs offset in each case by 180° with respect tothe stator angle.
 5. The method according to claim 1, wherein thedetermination of the initial estimated value for the rotor angle of thesynchronous machine comprises the formation of the mean value of thefirst and second estimated values involved in the smallest difference.6. The method according to claim 5, wherein the synchronous machinecomprises a non-salient-pole machine, and wherein at least two initialvoltage pulses, which bring the non-salient-pole machine intosaturation, are fed into the stator of the non-salient-pole machine. 7.The method according to claim 2, wherein the first and second estimatedcurves each comprise linear regression curves.
 8. A control device forestablishing the rotor angle of a synchronous machine, wherein thecontrol device is designed to carry out a method according to claim 1.9. An electric drive system, comprising: a control device according toclaim 8; and a synchronous machine, which is coupled to the controldevice, wherein the control device is designed to control thesynchronous machine in accordance with the established rotor angle.